On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

Original languageEnglish
Pages (from-to)1089-1138
Number of pages50
JournalJournal of Dynamics and Differential Equations
Volume25
Issue number4
DOIs
Publication statusPublished - 2013

Fingerprint

State-dependent Delay
Time Lag
Differentiability
Monotone
State Space
Strictly
Differential equation
First-order
Norm
Dependent
Class

Keywords

  • Delay differential equation
  • Differentiability with respect to parameters
  • State-dependent delay

ASJC Scopus subject areas

  • Analysis

Cite this

@article{9c3413dd845c4e1a9b1a5bcccab6378f,
title = "On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays",
abstract = "In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.",
keywords = "Delay differential equation, Differentiability with respect to parameters, State-dependent delay",
author = "F. Hartung",
year = "2013",
doi = "10.1007/s10884-013-9330-5",
language = "English",
volume = "25",
pages = "1089--1138",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays

AU - Hartung, F.

PY - 2013

Y1 - 2013

N2 - In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

AB - In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

KW - Delay differential equation

KW - Differentiability with respect to parameters

KW - State-dependent delay

UR - http://www.scopus.com/inward/record.url?scp=84890438101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890438101&partnerID=8YFLogxK

U2 - 10.1007/s10884-013-9330-5

DO - 10.1007/s10884-013-9330-5

M3 - Article

VL - 25

SP - 1089

EP - 1138

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 4

ER -